Population pharmacokinetics is concerned with modeling the processes of drug absorption, distribution, and elimination and their variability within a population, and is becoming increasingly important in drug development. In previous work, the only source of error which has been included in order to account for the difference between the measured drug concentration and the model prediction is measurement error in the drug concentration. The aim of this research is to extend the modeling to include random model error, for example, due to random error in the drug dose or random fluctuations in the pharmacokinetic parameters. In contrast to measurement error, which gives rise to uncorrelated errors at different measurement times within an individual, random model error induces correlations in the errors at different measurement times within an individual. In this work the effect of random model error on the difference between the measured drug concentration and the model prediction will be derived. Population data will be simulated including both measurement error and random model error. Modern computationally intensive mathematical methods (Markov chain Monte Carlo methods) will be generalized to estimate the population pharmacokinetic parameters as well as the parameters characterizing the sources of error from this simulated data. Finally, after such testing, the methods will be applied to real biomedical data supplied by researchers at the City of Hope.